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*From*: "Ugur Y. Yavuz" <uguryagmuryavuz@xxxxxxxxx>*Date*: Mon, 8 Jul 2024 07:48:54 -0700 (PDT)

Hello, I have a question about the prime operator, particularly how it gets parsed in conjunction with user-defined operators.

Consider the following operator definition, where pc and l are among the variables of the specification, and ProcSet is a constant:

WellFormed(IdxSet) ==

\A p \in ProcSet :

**CASE** pc[p] = "L0" -> TRUE

[] pc[p] = "L1" /\ l[p] \in IdxSet -> TRUE

[] pc[p] = "L1" /\ l[p] \notin IdxSet -> FALSE

\A p \in ProcSet :

[] pc[p] = "L1" /\ l[p] \in IdxSet -> TRUE

[] pc[p] = "L1" /\ l[p] \notin IdxSet -> FALSE

Note that we have:

WellFormed(IdxSet)' =

\A p \in ProcSet :

**CASE** pc'[p] = "L0" -> TRUE

[] pc'[p] = "L1" /\ l'[p] in IdxSet -> TRUE

[] pc'[p] = "L1" /\ l'[p] \notin IdxSet -> FALSE

Suppose L and A are also variables of the specification, and that we aim to prove the invariant \E IdxSet \in**SUBSET** 0..L-1 : WellFormed(IdxSet) in TLAPS. After proving it for the initial configuration, we need to prove it for a subsequent configuration, reached from one where the inductive invariant holds; i.e., \E IdxSet \in **SUBSET** 0..L'-1 : WellFormed(IdxSet)'. Suppose the witness for this claim needs to be a function of the specification variables' values in the next configuration. Say we want to proceed as follows:

\A p \in ProcSet :

[] pc'[p] = "L1" /\ l'[p] in IdxSet -> TRUE

[] pc'[p] = "L1" /\ l'[p] \notin IdxSet -> FALSE

Suppose L and A are also variables of the specification, and that we aim to prove the invariant \E IdxSet \in

...

<3>**DEFINE** full_indices == {idx \in 0..(L'-1) : A'[idx] > 0}

<3>1. WellFormed(full_indices)'

<3>

<3>1. WellFormed(full_indices)'

However, this results in a parser error: "Level error in applying operator ': The level of argument 1 exceeds the maximum level allowed by the operator."

Is this intended behavior? The _expression_ seems equivalent to:

Is this intended behavior? The _expression_ seems equivalent to:

\A p \in ProcSet :

**CASE** pc'[p] = "L0" -> TRUE

[] pc'[p] = "L1" /\ l'[p] in {idx \in 0..(L'-1) : A'[idx] > 0} -> TRUE

[] pc'[p] = "L1" /\ l'[p] \notin {idx \in 0..(L'-1) : A'[idx] > 0} -> FALSE

[] pc'[p] = "L1" /\ l'[p] in {idx \in 0..(L'-1) : A'[idx] > 0} -> TRUE

[] pc'[p] = "L1" /\ l'[p] \notin {idx \in 0..(L'-1) : A'[idx] > 0} -> FALSE

which I can express in TLA+. This issue arose in a larger proof, and I simplified it as much as possible. I circumvented it with several rewrites, which I believe shouldn't be necessary at a first glance. I can provide more context if needed.

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**Follow-Ups**:**[tlaplus] Re: Parsing issues with prime operator in user-defined operators***From:*Damien Doligez

**[tlaplus] Re: Parsing issues with prime operator in user-defined operators***From:*Andrew Helwer

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